= = b = 1 σ y = = 0.001
|
|
- Maud Casey
- 6 years ago
- Views:
Transcription
1 Econ 250 Fall 2007 s for Assignment 1 1. A local TV station advertises two news-casting positions. If three women (W 1, W 2, W 3 and two men (M 1, M 2 apply what is the sample space of the experiment of hiring two coanchors? Does it matter here that the positions being filled are equivalent? What is the probability that both men get the job? We have to choose two anchors among five individuals. So the experiment effectively entails choosing two elements (without replacement from the following set (W 1, W 2, W 3, M 1, M 2. Thus the sample space is: S {(W 1, W 2, (W 1, W 3, (W 2, W 3, (W 1, M 1, (W 1, M 2, (W 2, M 1, (W 2, M 2, (W 3, M 1, (W 3, M 2, (M 1, M 2 } as there are C possibilities. The probability that both men get the job is the probability of the outcome (M 1, M 2 which is just 1/10. It does matter that the two positions being filled are equivalent. If the station were seeking to hire, say, a sports announcer and a weather forecaster, the number of possible outcomes would be P 5 2 ( 20 as (W 2, M 1, for example, would represent a different staffing assignment than (M 1, W Consider the linear transformation Y i a bx i Suppose µ x 25 and σ x.05 and you want to have µ y 55 and σ y (i What values should a and b take? (ii Show what the appropriate transform on Y i is to take it tostandardized form (i.e. µ z 0 and σ z 1 (i µ y a bµ x and σ y b σ x. Thus, b σ y /σ x 1000/ taking the positive root. Then a µ y bµ x 55 (20000( (ii Note that: Z Y µ y, thus σ y a µ y σ y b 1 σ y You are given information on the annual returns of thirty stocks. 10%, 8%, 14%, 18%, 1%, 5%, 4%, 4%, 7%, 5%, 17%, 27%, 8%, 0%, 5%, %, 12%, 16%, 1%, 2% %, 5%, 16%, 22%, 15%, 18%, 3%, 5%, 8%, 4% 1
2 (i Draw a box plot for this sample of returns and interpret the box plot. (ii Calculate the sample mean, sample standard deviation for this sample of bond returns. What is the coefficient of variation and interpret. (i Q 1 0, Q 2 5 and Q (ii X , s.538 and CV Consolidated Industries has come under considerable pressure to eliminate its seemingly discriminatory hiring practices. Company officials have agreed that during the next five years, 60% of their new employees will be females and 30% will be minorities. One out of four new employees, though, will be white males. Is this a plausible probability statement. Why or why not? What percentage of their new hires will be minority females? P(male 1 P(female (we are assuming that a person can be either male or female but not both. Now, P(male P(male minorityp(male white as males can either be white or minorities. Then using P(male white 0.25, we have that P(male minority Now, P(minority P(male minorityp(female minority 0.3, since minorities can only be male or female. Therefore P(female minority Let random variables X, Y have the joint distribution given be the following table: Y X /48 0 b 1 0 5/48 8/48 2 a 0 /48 3 5/48 12/48 0 (i Find a and b if it is known that P(X Y 1/3. Show all work (ii Find the joint probability table for: P(XY (i P(X Y P(X 2, Y P(X 3, Y 3 a 12/48 1/3. Thus, a 4/48. (ii All the entries in the joint distribution table have to sum to 1. Hence, given the value we calculated above for a, it must be that b is equal to 2/48. 2
3 6. Six fair dice are rolled at once. What is the probability that each of the six faces appears? The number of ways each of the six faces can appear when six dice are rolled is simply equal to all the re-arrangements of {1, 2, 3, 4, 5, 6}. That is, a total of 6! ways. The size of the sample space is of course 6 6. Therefore, the required probability is 6! Suppose each of 10 sticks is broken into a long part and a short part. The 20 parts are arranged into 10 pairs and glued back together, so that again there are 10 sticks. What is the probability that each long part will be paired with a short part? (This problem is a model for the effects of radiation on a living cell. Each chromosome, as a result of being struck by ionizing radiation, breaks into two parts, one part containing the centromere. The cell will die unless the fragment containing the centromere recombines with one not containing a centromere. The total number of ways the 20 broken parts can be recombined into pairs is simply ( That is, its the same problem as choosing ten parts from a total of 20 without replacement (Why?. Now, the number of ways in which all the broken parts can be recombined and stay matched is Hence, the desired probability is ( Urn I contains five red chips and four white chips; urn II contains four red and five white chips. Two chips are to be transferred from urn I to urn II (i.e. drawn randomly from urn I and placed into urn II. Then a single chip is to be drawn from urn II. What is the probability that the chip drawn from the second urn will be white? Explain the sample space. Let B be the event White chip is drawn from urn II. Let A i, i 0, 1, 2, denote the event i white chips are transferred from urn I to urn II. Then, using the properties of conditional probabilities, P(B P(B A 0 P(A 0 P(B A 1 P(A 1 P(B A 2 P(A 2 Note that P(B A i (5 i/ and that P(A i is given by the hypergeometric distribution formula. Therefore, ( 5 P(B ( 5 53 ( 5 ( 0( 6 ( 10 ( 6 ( 5 ( 1( 1 7 ( 20 ( 7 ( 5 2( 0 ( 6. Suppose that a randomly selected group of k people are brought together. What is the probability that exactly one pair has the same birthday? Start with k 2, then k 3 and so on to see if you can recognize a pattern to write out the general formula 3
4 in terms of k. If we had 30 people in the room what is the probability that at least one has the same birthday? Picture the k individuals lined up in a row to form an ordered sequence. Omitting leap years, each person might have any one of 5 possible birthdays. Thus, by the multiplication rule, the group as a whole generates a sample space of 5 k birthday sequences. Now, define A to be the event at least two people have the same birthday. If each person is assumed to have the same chance of being born on any given day, the 5 k sequences are equally likely and P(A Number of sequences in A 5 k Counting the number of sequences in the numerator here is prohibitively difficult because of the complexity of the event A. However, counting the number of sequences A C is quite easy. Notice that each birthday sequence in the sample space belongs to exactly one of two categories: (a At least two people have the same birthday (b All k people have different birthdays Therefore, Number of sequences in A 5 k number of sequences where all k people have different birthdays The number of ways to form birthday sequences for k people subject to the restriction that all k birthdays must be different is simply the number of ways to form permutations of length k from a set of 5 distinct objects: Therefore, (5(4...(5 k 1 P(A P(at least two people have the same birthday 5k (5(4...(5 k 1 5 k For k 30, the probability is or nearly 71%! Now, let B be the event exactly two people have the same birthday. That is, we want all the sequences where there is exactly one duplicate. Then, the number of such sequences is ( k (5(4...(5 k 2 Using the same reasoning as before: P(B P(exactly two people have the same birthday ( k 2 (5(4...(5 k 5 k 4
5 10. Suppose a certain drug test is % accurate, that is, the test will correctly identify a drug user as testing positive % of the time, and will correctly identify a non-user as testing negative % of the time. Let s assume a corporation (say the Atlanta Falcons decides to test its employees for opium use, and 5% of the employees use the drug. Calculate the probability that, given a positive drug test, an employee is actually a drug user. We have, P( positive test drug user 0. P( positive test not a drug user 0.01 P( negative test drug user 0.01 P( negative test not a drug user 0. and P(employee is a drug user 0.05 Now, in order to compute P(employee is a drug user positive test we can use Bayes rule: P(drug user pos. test P(pos. test drug userp(drug user P(pos. test P(pos. test drug user P(drug user P(pos. test not drug user P(not drug user
(c) The probability that a randomly selected driver having a California drivers license
Statistics Test 2 Name: KEY 1 Classify each statement as an example of classical probability, empirical probability, or subjective probability (a An executive for the Krusty-O cereal factory makes an educated
More informationSome Discrete Distribution Families
Some Discrete Distribution Families ST 370 Many families of discrete distributions have been studied; we shall discuss the ones that are most commonly found in applications. In each family, we need a formula
More informationChapter 7 Study Guide: The Central Limit Theorem
Chapter 7 Study Guide: The Central Limit Theorem Introduction Why are we so concerned with means? Two reasons are that they give us a middle ground for comparison and they are easy to calculate. In this
More informationA probability distribution shows the possible outcomes of an experiment and the probability of each of these outcomes.
Introduction In the previous chapter we discussed the basic concepts of probability and described how the rules of addition and multiplication were used to compute probabilities. In this chapter we expand
More informationMATH 446/546 Homework 1:
MATH 446/546 Homework 1: Due September 28th, 216 Please answer the following questions. Students should type there work. 1. At time t, a company has I units of inventory in stock. Customers demand the
More informationMath 160 Professor Busken Chapter 5 Worksheets
Math 160 Professor Busken Chapter 5 Worksheets Name: 1. Find the expected value. Suppose you play a Pick 4 Lotto where you pay 50 to select a sequence of four digits, such as 2118. If you select the same
More informationDiscrete Random Variables
Discrete Random Variables MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives During this lesson we will learn to: distinguish between discrete and continuous
More informationDiscrete Random Variables
Discrete Random Variables MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Objectives During this lesson we will learn to: distinguish between discrete and continuous
More informationProblem Set 07 Discrete Random Variables
Name Problem Set 07 Discrete Random Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the random variable. 1) The random
More informationMATH 264 Problem Homework I
MATH Problem Homework I Due to December 9, 00@:0 PROBLEMS & SOLUTIONS. A student answers a multiple-choice examination question that offers four possible answers. Suppose that the probability that the
More informationRandom Variables and Applications OPRE 6301
Random Variables and Applications OPRE 6301 Random Variables... As noted earlier, variability is omnipresent in the business world. To model variability probabilistically, we need the concept of a random
More informationExperimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes
MDM 4U Probability Review Properties of Probability Experimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes Theoretical
More informationINSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS. 20 th May Subject CT3 Probability & Mathematical Statistics
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 20 th May 2013 Subject CT3 Probability & Mathematical Statistics Time allowed: Three Hours (10.00 13.00) Total Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1.
More informationSection 7.5 The Normal Distribution. Section 7.6 Application of the Normal Distribution
Section 7.6 Application of the Normal Distribution A random variable that may take on infinitely many values is called a continuous random variable. A continuous probability distribution is defined by
More informationUnit 04 Review. Probability Rules
Unit 04 Review Probability Rules A sample space contains all the possible outcomes observed in a trial of an experiment, a survey, or some random phenomenon. The sum of the probabilities for all possible
More informationDiscrete Random Variables
Discrete Random Variables ST 370 A random variable is a numerical value associated with the outcome of an experiment. Discrete random variable When we can enumerate the possible values of the variable
More informationPart 10: The Binomial Distribution
Part 10: The Binomial Distribution The binomial distribution is an important example of a probability distribution for a discrete random variable. It has wide ranging applications. One readily available
More informationCopyright 2011 Pearson Education, Inc. Publishing as Addison-Wesley.
Appendix: Statistics in Action Part I Financial Time Series 1. These data show the effects of stock splits. If you investigate further, you ll find that most of these splits (such as in May 1970) are 3-for-1
More informationDiscrete Probability Distributions
Discrete Probability Distributions Chapter 6 Learning Objectives Define terms random variable and probability distribution. Distinguish between discrete and continuous probability distributions. Calculate
More informationThe Binomial Distribution
AQR Reading: Binomial Probability Reading #1: The Binomial Distribution A. It would be very tedious if, every time we had a slightly different problem, we had to determine the probability distributions
More informationLearning Goals: * Determining the expected value from a probability distribution. * Applying the expected value formula to solve problems.
Learning Goals: * Determining the expected value from a probability distribution. * Applying the expected value formula to solve problems. The following are marks from assignments and tests in a math class.
More informationTheoretical Foundations
Theoretical Foundations Probabilities Monia Ranalli monia.ranalli@uniroma2.it Ranalli M. Theoretical Foundations - Probabilities 1 / 27 Objectives understand the probability basics quantify random phenomena
More informationMath 21 Test
Math 21 Test 2 010705 Name Show all your work for each problem in the space provided. Correct answers without work shown will earn minimum credit. You may use your calculator. 1. [6 points] The sample
More informationPart 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going?
1 The Law of Averages The Expected Value & The Standard Error Where Are We Going? Sums of random numbers The law of averages Box models for generating random numbers Sums of draws: the Expected Value Standard
More informationProbability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7
Probability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7 Lew Davidson (Dr.D.) Mallard Creek High School Lewis.Davidson@cms.k12.nc.us 704-786-0470 Probability & Sampling The Practice of Statistics
More informationTRUE-FALSE: Determine whether each of the following statements is true or false.
Chapter 6 Test Review Name TRUE-FALSE: Determine whether each of the following statements is true or false. 1) A random variable is continuous when the set of possible values includes an entire interval
More information6.1 Binomial Theorem
Unit 6 Probability AFM Valentine 6.1 Binomial Theorem Objective: I will be able to read and evaluate binomial coefficients. I will be able to expand binomials using binomial theorem. Vocabulary Binomial
More information4.1 Probability Distributions
Probability and Statistics Mrs. Leahy Chapter 4: Discrete Probability Distribution ALWAYS KEEP IN MIND: The Probability of an event is ALWAYS between: and!!!! 4.1 Probability Distributions Random Variables
More informationMath 14 Lecture Notes Ch. 4.3
4.3 The Binomial Distribution Example 1: The former Sacramento King's DeMarcus Cousins makes 77% of his free throws. If he shoots 3 times, what is the probability that he will make exactly 0, 1, 2, or
More informationThe Binomial Distribution
MATH 382 The Binomial Distribution Dr. Neal, WKU Suppose there is a fixed probability p of having an occurrence (or success ) on any single attempt, and a sequence of n independent attempts is made. Then
More information7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4
7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4 - Would the correlation between x and y in the table above be positive or negative? The correlation is negative. -
More informationMidterm Exam III Review
Midterm Exam III Review Dr. Joseph Brennan Math 148, BU Dr. Joseph Brennan (Math 148, BU) Midterm Exam III Review 1 / 25 Permutations and Combinations ORDER In order to count the number of possible ways
More informationChapter 9. Sampling Distributions. A sampling distribution is created by, as the name suggests, sampling.
Chapter 9 Sampling Distributions 9.1 Sampling Distributions A sampling distribution is created by, as the name suggests, sampling. The method we will employ on the rules of probability and the laws of
More informationSimple Random Sample
Simple Random Sample A simple random sample (SRS) of size n consists of n elements from the population chosen in such a way that every set of n elements has an equal chance to be the sample actually selected.
More informationChapter 6: Probability: What are the Chances?
+ Chapter 6: Probability: What are the Chances? Section 6.1 Randomness and Probability The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE + Section 6.1 Randomness and Probability Learning
More informationProbability Distributions
4.1 Probability Distributions Random Variables A random variable x represents a numerical value associated with each outcome of a probability distribution. A random variable is discrete if it has a finite
More informationPROBABILITY DISTRIBUTIONS
CHAPTER 3 PROBABILITY DISTRIBUTIONS Page Contents 3.1 Introduction to Probability Distributions 51 3.2 The Normal Distribution 56 3.3 The Binomial Distribution 60 3.4 The Poisson Distribution 64 Exercise
More informationMAKING SENSE OF DATA Essentials series
MAKING SENSE OF DATA Essentials series THE NORMAL DISTRIBUTION Copyright by City of Bradford MDC Prerequisites Descriptive statistics Charts and graphs The normal distribution Surveys and sampling Correlation
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Shade the Venn diagram to represent the set. 1) B A 1) 2) (A B C')' 2) Determine whether the given events
More informationHave you ever wondered whether it would be worth it to buy a lottery ticket every week, or pondered on questions such as If I were offered a choice
Section 8.5: Expected Value and Variance Have you ever wondered whether it would be worth it to buy a lottery ticket every week, or pondered on questions such as If I were offered a choice between a million
More informationII - Probability. Counting Techniques. three rules of counting. 1multiplication rules. 2permutations. 3combinations
II - Probability Counting Techniques three rules of counting 1multiplication rules 2permutations 3combinations Section 2 - Probability (1) II - Probability Counting Techniques 1multiplication rules In
More information3.2 Binomial and Hypergeometric Probabilities
3.2 Binomial and Hypergeometric Probabilities Ulrich Hoensch Wednesday, January 23, 2013 Example An urn contains ten balls, exactly seven of which are red. Suppose five balls are drawn at random and with
More information7.1: Sets. What is a set? What is the empty set? When are two sets equal? What is set builder notation? What is the universal set?
7.1: Sets What is a set? What is the empty set? When are two sets equal? What is set builder notation? What is the universal set? Example 1: Write the elements belonging to each set. a. {x x is a natural
More informationSTUDY SET 1. Discrete Probability Distributions. x P(x) and x = 6.
STUDY SET 1 Discrete Probability Distributions 1. Consider the following probability distribution function. Compute the mean and standard deviation of. x 0 1 2 3 4 5 6 7 P(x) 0.05 0.16 0.19 0.24 0.18 0.11
More informationPreviously, when making inferences about the population mean, μ, we were assuming the following simple conditions:
Chapter 17 Inference about a Population Mean Conditions for inference Previously, when making inferences about the population mean, μ, we were assuming the following simple conditions: (1) Our data (observations)
More information8.1 Binomial Distributions
8.1 Binomial Distributions The Binomial Setting The 4 Conditions of a Binomial Setting: 1.Each observation falls into 1 of 2 categories ( success or fail ) 2 2.There is a fixed # n of observations. 3.All
More informationBinomial Distributions
Binomial Distributions Binomial Experiment The experiment is repeated for a fixed number of trials, where each trial is independent of the other trials There are only two possible outcomes of interest
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives After this lesson we will be able to: determine whether a probability
More informationBusiness Statistics. Chapter 5 Discrete Probability Distributions QMIS 120. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 5 Discrete Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should
More informationPart V - Chance Variability
Part V - Chance Variability Dr. Joseph Brennan Math 148, BU Dr. Joseph Brennan (Math 148, BU) Part V - Chance Variability 1 / 78 Law of Averages In Chapter 13 we discussed the Kerrich coin-tossing experiment.
More information2017 Fall QMS102 Tip Sheet 2
Chapter 5: Basic Probability 2017 Fall QMS102 Tip Sheet 2 (Covering Chapters 5 to 8) EVENTS -- Each possible outcome of a variable is an event, including 3 types. 1. Simple event = Described by a single
More information1. You roll a six sided die two times. What is the probability that you do not get a three on either roll? 5/6 * 5/6 = 25/36.694
Math 107 Review for final test 1. You roll a six sided die two times. What is the probability that you do not get a three on either roll? 5/6 * 5/6 = 25/36.694 2. Consider a box with 5 blue balls, 7 red
More informationDistribution of the Sample Mean
Distribution of the Sample Mean MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Experiment (1 of 3) Suppose we have the following population : 4 8 1 2 3 4 9 1
More informationChapter 5 Student Lecture Notes 5-1. Department of Quantitative Methods & Information Systems. Business Statistics
Chapter 5 Student Lecture Notes 5-1 Department of Quantitative Methods & Information Systems Business Statistics Chapter 5 Discrete Probability Distributions QMIS 120 Dr. Mohammad Zainal Chapter Goals
More informationProbability and Sample space
Probability and Sample space We call a phenomenon random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions. The probability of any outcome
More informationDetermine whether the given events are disjoint. 1) Drawing a face card from a deck of cards and drawing a deuce A) Yes B) No
Assignment 8.-8.6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given events are disjoint. 1) Drawing a face card from
More information4.2 Bernoulli Trials and Binomial Distributions
Arkansas Tech University MATH 3513: Applied Statistics I Dr. Marcel B. Finan 4.2 Bernoulli Trials and Binomial Distributions A Bernoulli trial 1 is an experiment with exactly two outcomes: Success and
More informationUniform Probability Distribution. Continuous Random Variables &
Continuous Random Variables & What is a Random Variable? It is a quantity whose values are real numbers and are determined by the number of desired outcomes of an experiment. Is there any special Random
More information6. THE BINOMIAL DISTRIBUTION
6. THE BINOMIAL DISTRIBUTION Eg: For 1000 borrowers in the lowest risk category (FICO score between 800 and 850), what is the probability that at least 250 of them will default on their loan (thereby rendering
More informationSection 6.5. The Central Limit Theorem
Section 6.5 The Central Limit Theorem Idea Will allow us to combine the theory from 6.4 (sampling distribution idea) with our central limit theorem and that will allow us the do hypothesis testing in the
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 4 Random Variables & Probability Distributions Content 1. Two Types of Random Variables 2. Probability Distributions for Discrete Random Variables 3. The Binomial
More informationChapter 5: Probability
Chapter 5: These notes reflect material from our text, Exploring the Practice of Statistics, by Moore, McCabe, and Craig, published by Freeman, 2014. quantifies randomness. It is a formal framework with
More informationMath 13 Statistics Fall 2014 Midterm 2 Review Problems. Due on the day of the midterm (Friday, October 3, 2014 at 6 p.m. in N12)
Math 13 Statistics Fall 2014 Midterm 2 Review Problems Due on the day of the midterm (Friday, October 3, 2014 at 6 p.m. in N12) PRINT NAME (ALL UPPERCASE): Problem 1: A couple wants to have three babies
More informationChapter 3 - Lecture 5 The Binomial Probability Distribution
Chapter 3 - Lecture 5 The Binomial Probability October 12th, 2009 Experiment Examples Moments and moment generating function of a Binomial Random Variable Outline Experiment Examples A binomial experiment
More informationSTAT 3090 Test 2 - Version B Fall Student s Printed Name: PLEASE READ DIRECTIONS!!!!
Student s Printed Name: Instructor: XID: Section #: Read each question very carefully. You are permitted to use a calculator on all portions of this exam. You are NOT allowed to use any textbook, notes,
More informationChapter 8. Binomial and Geometric Distributions
Chapter 8 Binomial and Geometric Distributions Lesson 8-1, Part 1 Binomial Distribution What is a Binomial Distribution? Specific type of discrete probability distribution The outcomes belong to two categories
More informationCD Appendix F Hypergeometric Distribution
D Appendix F Hypergeometric Distribution A hypergeometric experiment is an experiment where a sample of n items is taen without replacement from a finite population of items, each of which is classified
More informationProbability Distribution Unit Review
Probability Distribution Unit Review Topics: Pascal's Triangle and Binomial Theorem Probability Distributions and Histograms Expected Values, Fair Games of chance Binomial Distributions Hypergeometric
More informationInstructor: A.E.Cary. Math 243 Exam 2
Name: Instructor: A.E.Cary Instructions: Show all your work in a manner consistent with that demonstrated in class. Round your answers where appropriate. Use 3 decimal places when rounding answers. In
More informationA.REPRESENTATION OF DATA
A.REPRESENTATION OF DATA (a) GRAPHS : PART I Q: Why do we need a graph paper? Ans: You need graph paper to draw: (i) Histogram (ii) Cumulative Frequency Curve (iii) Frequency Polygon (iv) Box-and-Whisker
More informationExamples: On a menu, there are 5 appetizers, 10 entrees, 6 desserts, and 4 beverages. How many possible dinners are there?
Notes Probability AP Statistics Probability: A branch of mathematics that describes the pattern of chance outcomes. Probability outcomes are the basis for inference. Randomness: (not haphazardous) A kind
More informationChapter Six Probability Distributions
6.1 Probability Distributions Discrete Random Variable Chapter Six Probability Distributions x P(x) 2 0.08 4 0.13 6 0.25 8 0.31 10 0.16 12 0.01 Practice. Construct a probability distribution for the number
More informationReview. What is the probability of throwing two 6s in a row with a fair die? a) b) c) d) 0.333
Review In most card games cards are dealt without replacement. What is the probability of being dealt an ace and then a 3? Choose the closest answer. a) 0.0045 b) 0.0059 c) 0.0060 d) 0.1553 Review What
More information4.2 Probability Distributions
4.2 Probability Distributions Definition. A random variable is a variable whose value is a numerical outcome of a random phenomenon. The probability distribution of a random variable tells us what the
More informationMATH1215: Mathematical Thinking Sec. 08 Spring Worksheet 9: Solution. x P(x)
N. Name: MATH: Mathematical Thinking Sec. 08 Spring 0 Worksheet 9: Solution Problem Compute the expected value of this probability distribution: x 3 8 0 3 P(x) 0. 0.0 0.3 0. Clearly, a value is missing
More informationTest 6A AP Statistics Name:
Test 6A AP Statistics Name: Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A marketing survey compiled data on the number of personal computers in households. If X = the
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 131-03 Practice Questions for Exam# 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) What is the effective rate that corresponds to a nominal
More informationECON 214 Elements of Statistics for Economists 2016/2017
ECON 214 Elements of Statistics for Economists 2016/2017 Topic The Normal Distribution Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College of Education School of Continuing and
More informationChapter 4 Discrete Random variables
Chapter 4 Discrete Random variables A is a variable that assumes numerical values associated with the random outcomes of an experiment, where only one numerical value is assigned to each sample point.
More informationAP Statistics Section 6.1 Day 1 Multiple Choice Practice. a) a random variable. b) a parameter. c) biased. d) a random sample. e) a statistic.
A Statistics Section 6.1 Day 1 ultiple Choice ractice Name: 1. A variable whose value is a numerical outcome of a random phenomenon is called a) a random variable. b) a parameter. c) biased. d) a random
More informationFormula for the Multinomial Distribution
6 5 Other Types of Distributions (Optional) In addition to the binomial distribution, other types of distributions are used in statistics. Three of the most commonly used distributions are the multinomial
More informationNORMAL RANDOM VARIABLES (Normal or gaussian distribution)
NORMAL RANDOM VARIABLES (Normal or gaussian distribution) Many variables, as pregnancy lengths, foot sizes etc.. exhibit a normal distribution. The shape of the distribution is a symmetric bell shape.
More informationExercises for Chapter (5)
Exercises for Chapter (5) MULTILE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) 500 families were interviewed and the number of children per family was
More informationList of Online Quizzes: Quiz7: Basic Probability Quiz 8: Expectation and sigma. Quiz 9: Binomial Introduction Quiz 10: Binomial Probability
List of Online Homework: Homework 6: Random Variables and Discrete Variables Homework7: Expected Value and Standard Dev of a Variable Homework8: The Binomial Distribution List of Online Quizzes: Quiz7:
More informationEXERCISES FOR PRACTICE SESSION 2 OF STAT CAMP
EXERCISES FOR PRACTICE SESSION 2 OF STAT CAMP Note 1: The exercises below that are referenced by chapter number are taken or modified from the following open-source online textbook that was adapted by
More informationMA 1125 Lecture 14 - Expected Values. Wednesday, October 4, Objectives: Introduce expected values.
MA 5 Lecture 4 - Expected Values Wednesday, October 4, 27 Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
More informationHomework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a Announcements: There are some office hour changes for Nov 5, 8, 9 on website Week 5 quiz begins after class today and ends at
More informationProbability: Week 4. Kwonsang Lee. University of Pennsylvania February 13, 2015
Probability: Week 4 Kwonsang Lee University of Pennsylvania kwonlee@wharton.upenn.edu February 13, 2015 Kwonsang Lee STAT111 February 13, 2015 1 / 21 Probability Sample space S: the set of all possible
More informationExample 1: Find the equation of the line containing points (1,2) and (2,3).
Example 1: Find the equation of the line containing points (1,2) and (2,3). Example 2: The Ace Company installed a new machine in one of its factories at a cost of $20,000. The machine is depreciated linearly
More informationMANAGEMENT PRINCIPLES AND STATISTICS (252 BE)
MANAGEMENT PRINCIPLES AND STATISTICS (252 BE) Normal and Binomial Distribution Applied to Construction Management Sampling and Confidence Intervals Sr Tan Liat Choon Email: tanliatchoon@gmail.com Mobile:
More information2.) What is the set of outcomes that describes the event that at least one of the items selected is defective? {AD, DA, DD}
Math 361 Practice Exam 2 (Use this information for questions 1 3) At the end of a production run manufacturing rubber gaskets, items are sampled at random and inspected to determine if the item is Acceptable
More informationChapter 5. Discrete Probability Distributions. McGraw-Hill, Bluman, 7 th ed, Chapter 5 1
Chapter 5 Discrete Probability Distributions McGraw-Hill, Bluman, 7 th ed, Chapter 5 1 Chapter 5 Overview Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation, and Expectation
More informationCHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Binomial and Geometric Random
More informationBinomial Distributions
Binomial Distributions (aka Bernouli s Trials) Chapter 8 Binomial Distribution an important class of probability distributions, which occur under the following Binomial Setting (1) There is a number n
More informationChpt The Binomial Distribution
Chpt 5 5-4 The Binomial Distribution 1 /36 Chpt 5-4 Chpt 5 Homework p262 Applying the Concepts Exercises p263 1-11, 14-18, 23, 24, 26 2 /36 Objective Chpt 5 Find the exact probability for x successes in
More informationECON 214 Elements of Statistics for Economists
ECON 214 Elements of Statistics for Economists Session 7 The Normal Distribution Part 1 Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education
More informationCHAPTER 10: Introducing Probability
CHAPTER 10: Introducing Probability The Basic Practice of Statistics 6 th Edition Moore / Notz / Fligner Lecture PowerPoint Slides Chapter 10 Concepts 2 The Idea of Probability Probability Models Probability
More informationExam 2 - Pretest DS-23
Exam 2 - Pretest DS-23 Chapter (4,5,6) Odds 10/3/2017 Ferbrache MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A single die
More informationRandom variables. Discrete random variables. Continuous random variables.
Random variables Discrete random variables. Continuous random variables. Discrete random variables. Denote a discrete random variable with X: It is a variable that takes values with some probability. Examples:
More informationStudy Guide: Chapter 5, Sections 1 thru 3 (Probability Distributions)
Study Guide: Chapter 5, Sections 1 thru 3 (Probability Distributions) Name SHORT ANSWER. 1) Fill in the missing value so that the following table represents a probability distribution. x 1 2 3 4 P(x) 0.09
More information